Graphical Abstract

Topological insulator (TI) is a new class of quantum materials which band structure

exhibits a nontrivial Z2 topology. Such materials possess a single Dirac cone located

inside the bulk bandgap and therefore the potential applications in the spintronics.

Mechanical exfoliation is a convenient method to prepare the mesoscale TI samples

inheriting the bulk crystalline structures, where a critical issue lies to locate the TI

flakes of interests. Optical reading has been demonstrated in the study of graphene.

Here we extend the approach to the study of mesoscale TI flakes. The left figure

shows the calculated contrast of Bi2Te3 flakes on a SiO2-capped silicon wafer. It is

confirmed by the experiment of the optical contrasts dependent on the thickness as

shown in the right right. One may see the contrast inversion in its inset. Please see the

detailed discussion in the text.

VisualizingVisualizingVisualizingVisualizing topologicaltopologicaltopologicaltopological insulatinginsulatinginsulatinginsulating BiBiBiBi2222TeTeTeTe3333 quintuplequintuplequintuplequintuple layerslayerslayerslayers onononon SiOSiOSiOSiO2222-capped-capped-capped-capped SiSiSiSi

substratessubstratessubstratessubstrates andandandand itsitsitsits contrastcontrastcontrastcontrast optimizationoptimizationoptimizationoptimization

Zhaoguo Li, Yuyuan Qin, Yuewen Mu, Taishi Chen, Changhui Xu, Longbing He,

Jianguo Wan, Fengqi Song*, Min Han, Guanghou Wang

Department of Physics and National Lab of Solid State Microstructures, Nanjing

University, 210093, Nanjing, P. R. China

Abstract: Thin Bi2Te3 flakes, with as few as 3 quintuple layers, are optically

visualized on the SiO2-capped Si substrates. Their optical contrasts vary with the

illumination wavelength, flake thickness and capping layers. The maximum contrast

appears at the optimized light with the 570nm wavelength. The contrast turns reversed

when the flake is reduced to less than 20 quintuple layers. A calculation based on the

Fresnel law describes the above observation with the constructions of the layer

number-wave length-contrast three-dimensional (3D) diagram and the cap thickness-

wavelength-contrast 3D diagram, applicative in the current studies of topological

insulating flakes.

* Corresponding author: songfengqi@nju.edu.cn

Bi2Te3, a narrow band-gap semiconductor, has been featured as a vital

component for the thermoelectric industry since the bulk Bi2Te3-based materials

possess the highest thermoelectric figure of merit (ZT~1.14) at room temperature1-5. It

has recently gained even more attention from the physics community after

demonstrated to be a 3D topological insulator (TI)6-8, which is a new state of quantum

matter with a prominent bulk energy gap and a conductive surface state

simultaneously9-11. Such a surface state even presents a Dirac cone in its electronic

structure12-13. Due to the entanglement between the carriers in the top and the bottom

layer, the TI behavior of Bi2Te3 exhibits the obvious dependence on the number of the

quintuple layers6,14, which thus expects precise layer control during the sample

preparation or relocating the nanosheets. The Bi2Te3 crystals is of the rhombohedral

structure, where five atomic layers (Te(1)-Bi-Te(2)-Bi-Te(1)) form a quintuple unit with

thickness ~1nm. Between two quintuple layers (QLs), the spacing is larger and the

weak van der Waals interaction (Te(1)-Te(1)) is dominant3,15. This creates a possibility

for producing quasi two-dimensional atomic quintuple layers by simple mechanical

exfoliations. Gently rubbing the layered materials against another stiff surface may

slice the crystal for few-layer materials as done in the graphene fabrication16. Such

exfoliation-based preparation remains critical since such slices have demonstrated

good crystalline structures and reliable carrier behaviors despite the fact that chemical

bath deposition17, solvothermalization18 and various evaporation techniques5 have

formed the Bi2Te3 crystals because these techniques normally produce polycrystalline

films for thermoelectric applications, far from the current TI studies9.

However, the exfoliated thin Bi2Te3 layers are often mixed with the flakes of

variable layer numbers15. Therefore an important issue for the exfoliated sample is to

locate the TI flakes of interests, on which modern microscopic techniques, including

atomic-force microscopy, scanning tunneling microscopy, and electron microscopy,

lose their efficiencies due to their extremely low throughput19-20. In the research of

graphene, an optically locating of the few-layer sheets on top of an oxidized Si wafer is

a critical step21-22. The thin flakes are transparent to the reflected light, which

contributes an additional optical path and changes their interference color contrast

with respect to an empty wafer. The thickness of the thin graphite flakes can therefore

be distinguished by reading their color contrast. Even the few-layer graphene can be

visible in this way 21-22. The optically-assisted locating is also applicable and a critical

step to isolate the TI sheets of interests in the exfoliated Bi2Te3 quintuple layers15,

while no extensive study is reported. Furthermore, such study of locating the sub-

wavelength-thick sheets by visible illumination microscopy is still of good interests in

elementary optics. Here we report the visualization of the exfoliated Bi2Te3 flakes,

with as few as 3 layers, by using the 300nm-thick silica capped silicon substrate and

visible illumination. A calculation based on the Fresnel optics is carried out with the

construction of the three-dimensional layer number-wave length-contrast diagram. The

predictions on the optimized incident wavelength and the contrast reversion are

largely confirmed by our experiment.

The Bi2Te3 thin sheets were prepared by a mechanical exfoliation procedure

similar to the graphene preparation16. Such sheets have been regarded as a TI

candidate recently3,14. A scotch tape with the crystalline Bi2Te3 powder (purchased

from Alfa Aesar, vacuum deposition grade, 99.999% (metals basis)) was folded many

times and then pressed onto the silica-capped wafer. The samples were then imaged by

a NTEGRA Probe NanoLaboratory system (NT-MDT, Co.), where the atomic force

microscopy (AFM) unit, optical imaging and confocal Raman scattering unit are

combined. Monochromatic illumination is implemented by narrow-band filters (with

the half widths of 10nm) as well as a few low-power lasers. FigureFigureFigureFigure 1111 shows a Bi2Te3

thin sheet with 10 quintuple layers, which thickness was measured by AFM (see Fig.

1a). Its composition is confirmed by the Raman scattering23. We can clearly see the

sheet on the silica-capped wafer upon the illumination of a blue laser (Fig.1b), while

we find it becomes invisible if using an empty wafer. We also see other sheets with as

few as 3 quintuple layers. This demonstrates the applicability of the visualization

technique22.

Such visualization can be described by the optical contrast driven by the

Fresnel’s Law21-22,24. We carried out the calculation, where the contrast is defined as

(1).)(

)()()(

/SiSiO

TeBi/SiSiO

2

322

λλλ

λR

RRC

−=

The function R(λ) ( ) is the reflected optical intensities with the light)()()( * λλλ rrR =

(wavelength of λ). d1 and d2 as defined in the right inset of FigureFigureFigureFigure 2a2a2a2a. The function

(2).)(32

)(31

)(21

)(

)(321

)(3

)(2

)(1

21212121

21212121

eeeeeeee)( ββββββββ

ββββββββ

λ −+−−−+

−+−−−+

++++++

= iiii

iiii

rrrrrrrrrrrrr

The parameters , , , and10

101 nn

nnr+−

=21

212 nn

nnr+−

=32

323 nn

nnr+−

= 1 11

2 n dπβ

λ=

are calculated if the complex refractive indexes n0, n1, n2, n3 (which2 22

2 n dπβ

λ=

correspond air, Bi2Te3, SiO2, Si, respectively and n1, n2, n3 depend on λ.) are given as in

the references21-22,25. The detailed complex refractive indexes are found to vary with

different samples with different crystalline conditions , the compositions and even the

substrates, where the experimental values need further interpolation5,26. Here the

complex refractive indexes of the Bi2Te3 crystal are therefore generated using the

Cambridge Sequential Total Energy Package27. The calculated refractive indexes are

largely the same as those adapted from the experiments on the thermal evaporated

samples except that the refractive index exhibits 50 percent larger fluctuation than that

of the experimental values (1-2)5,26. As a manifestation, we change the slope of the

wavelength–refractive index curve from 1/100 nm to 0, the optimal wavelength with

the maximized contrast is found to shift only 5 nm. Hence, the employment of the

simulated refraction indices introduced reasonable errors in the calculated contrast

functions, on which we can make comparisons to the experiments. The other refractive

indices (silica, silicon) were obtained from the reference book25. Fig. 2a and 2b show

the calculated diagram of the wavelength-thickness-contrast relation and the diagram

of the optical contrast plotted against the thickness of the capping layer and the

incident wavelength respectively. The optical contrast of the flake obviously changes

with both the light wavelength and flake thickness. We can see a common optimized

wavelength in Fig. 2a. The inset left in Fig. 2a show the relation of optical contrast

against the layer number with 570nm monochromatic light incidence. With the

increase of the quintuple layers, the contrast increased until six-quintuples which

reached the maximum contrast. Then, the contrast showed a decreased trend, and

saturated when quintuple layers larger than 80. Upon the changing of the thickness of

the capping layer, a few bands with the maximized contrast appear in Fig. 2b. The

bands cover a wide range of cap thickness from 70-130nm and 200-350nm etc. There

are effective contrasts in the light wavelength from 450nm to 640nm for our 300nm-

silica-capped wafer, guaranteeing the visibility of our thin flakes. We believe even the

contrast of a single quintuple layer may justify the detection by the CCD if the

incidence is intense enough.

The optical contrast of the sub-wavelength-thick flakes comes from the added

optical path lengths because of the difference of optical path length between Bi2Te3

and SiO2 when monochromatic light incidence as the difference of refractive index of

Bi2Te3 and SiO2. As the refractive indexes of Bi2Te3, SiO2 and Si dependent on λ and

therefore optical contrast presents a wavelength-dependent behavior. One of the

critical issues is to obtain an optimized wavelength with the maximized contrast. The

calculation shows the maximized optical contrasts fall in the wavelength region from

550-600nm whichever thickness of the TI flakes are imaged (Fig. 2a). We have also

mentioned the optimized wavelength is predicted to be independent on the variation of

the refractive indexes. Here illuminating the samples by the monochromatic light from

the narrow-band filters, with the center wavelengths at 570, 524 and 470nm, the

optical micrographs of a selected wafer with a few thick Bi2Te3 flakes are shown in

FigureFigureFigureFigure 3a3a3a3a, 3b and 3c respectively. There is a flake with the thickness of larger than

100nm as marked by the light arrow, and two thinner flakes (80 and 50nm respectively)

in the left down of the graph as measured by AFM. One can see the contrast

obviously increases with increasing the thickness in Fig 3a. The maximized contrasts

appear at 570nm for all the shown flakes. The highlighted flake is even invisible

during the illumination of 470nm (Fig 3c). The flakes are also invisible using the

illumination of incident light with the wavelength larger than 600nm. An optimized

illumination wavelength of 570nm that commonly provides maximized contrast is

shown.

It is quite prominent that the contrast turns reversed after the critical thickness

of 20nm as seen in Fig 2a. In the thinner region of more interests in the layer-

dependent TI behaviors, a saturated reversed contrast is predicted at 13nm (i.e. 13

quintuple layers). The value could be a bit inaccurate because the dielectric response

changes abruptly for the flake with a few quintuple layers5. The normal contrast

increases with increasing the flake thickness in the thicker region as observed in Fig. 3.

It is totally saturated at the thickness of larger than 80nm. Such contrast reversion can

experimentally be observed as shown in FigureFigureFigureFigure 4a4a4a4a, where a sample is illuminated by a

laser at 473nm. The image is obtained by the scanning confocal mode. The few-layer

TI sheets contribute much smaller contrast than the thick flakes, which is predicted to

be around a fifth (Fig 2a). Therefore, more intense source is required to feed the CCD

detector with a better signal/noise ratio than that with the filtered illuminations. AFM

measures the thickness of less than 30nm for the flakes as marked by the white arrows

in Fig 4a. The top one is 20nm thick and the below one is about 5 nm.As compared to

the flakes with the thickness of more than 50nm, one may see the contrast has been

reversed. After the contrast reversion, the thickness-contrast relation is no longer

monotonic. Please see Fig. 1 for the images of the 10nm-thick flake, which contrast is

even stronger than that of the 20nm-thick flake in Fig 4a. All the observations on the

thickness-contrast relation, both the monotonic increase of normal contrast and a

maximized reversed contrast, confirm the theory. We note that even the thin flakes

with as few as 3 quintuple layers can be located by this approach although the contrast

is extremely poor as also expected by the calculation shown in Fig. 2a. Therefore, the

present approach forms a reliable technique to distinguish the few-quintuple-layer

Bi2Te3 sheets by simply reading its contrast.

The applicable range and the error with the approach were assessed in order to

determine the thickness by the optical reading independently. Using the 473-nm-

wavlength laser, we measured dozens of samples for their optical contrast. The

thickness of the flakes were determined by AFM. The experiment data were plotted in

FigureFigureFigureFigure 4b4b4b4b, where we also show the simulated contrast curve using the first-principles

calculated refractive index nth=1.2-2.47i (the red-dot line). The black curve in Fig. 4b

was simulated using the experimentally-determined refractive index nexp=0.84-2.6i.

We can see the consistent trends of all the experimental and theoretical curves. All the

curves present a minimum contrast (nearly zero) in the range of 15-20 QLs. The

systematic deviation between the two calculated curves may be ascribed to the

different refractive index of the subwavelength-thick flakes from that of the bulk5. The

same source applies to the higher experimental contrasts for the few-layer flakes. An

applicable range of the approach is estabilished to be 5-50 QLs, above which no

resolvable difference can be measured. The flakes are no longer TIs below 5 layers14.

In the selected range, the contrast presents a monotone decrease with the increasing

QLs. The errors of such determinations are around 40 percent. The coarse approach

provides a critical and effective locating step in the study of TI Bi2Te3 flakes.

In summary, we have studied visualizing the sub-wavelength-thick Bi2Te3 flakes

by optical imaging the flakes on a capped Si wafer. The added optical length

contributes obvious contrast even for the flake with as few as 3 quintuple layers. We

obtain the layer number-wave length-contrast diagram and the wave length-cap

thickness -contrast diagrams of the thin Bi2Te3 flakes supported by a silica-capped Si

wafer by a calculation based on the Fresnel law. Both the optimized wavelength giving

a commonly maximized contrast and the thickness-dependent contrast reversion have

been demonstrated by our experiments. The present work distinguishes the few-

quintuple-layer Bi2Te3 sheets by simply reading its contrast during the 570nm

illumination and thus provides a critical locating step in the study of TI Bi2Te3 flakes.

We thank the National Natural Science Foundation of China (Grant numbers:

90606002, 11075076, and 10775070) and the National Key Projects for Basic

Research of China (Grant numbers: 2009CB930501, 2010CB923401) for supporting

this project. The Program for New Century Excellent Talents in University of China

Grant No. NCET-07-0422 is also acknowledged.

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FigureFigureFigureFigureCaptionCaptionCaptionCaption

FigureFigureFigureFigure 1111. A few-quintuple-layer Bi2Te3 flake. (a) is its AFM image and (b) is its

optical image. The inset in, (a) is its profile which correspond to the blue line. The

scale bars of (a) and (b) are 2μm. The edge of the flake is not sharp due to the fact that

the size of the flake is close to the diffraction limit.

FigureFigureFigureFigure 2222. The calculated optical contrast. (a). The calculated three-dimensional

diagram of the optical contrast of the Bi2Te3 film against the incident wavelength and

the membrane thickness (marked as height) when the cap silica is 300nm thick. The

inset left show the relation of optical contrast against the layer number with 570nm

monochromatic light incidence. The inset right is the experimental configuration. (b).

The calculated optical contrast of a quintuple layer is plotted against the silica

thickness and the incident wavelength.

FigureFigureFigureFigure 3333. Optical micrographs of a wafer with the TI flakes upon the illumination

by the white light filtered with the center wavelength of 570nm (a), 524nm (b) and

470nm(c). The white arrows mark the same Bi2Te3 flake for comparison. All the bars

are 20μm.

FigureFigureFigureFigure 4444. The contrast reversed with the thickness increase. (a). Optical micrograph of

a wafer with many Bi2Te3 flakes illuminated by a low-power blue laser. One can see

the reverse contrasts of some flakes marked by the arrows. The top one measures

20nm thick and the bottom one measures 5nm thick. The width of the micrograph is

around 70μm. (b). The experiment contrast against the quintuple layers (marked as

thickness) with a λ=473nm laser incident. The blue blocks , red-dot line and black line

correspond to the experiment data, first-principle calculation and semi-empirical

calculation, respectively.

LiLiLiLi etetetet alalalal FigFigFigFig 1111

LiLiLiLi etetetet alalalal ,,,, FigFigFigFig 2222

LiLiLiLi etetetet alalalal FigFigFigFig 3333

LiLiLiLi etetetet alalalal ,,,, FigFigFigFig 4444